\u00a9 2023 wikiHow, Inc. All rights reserved. The spring constant is determined using the value of the force applied and the displacement caused by Force on the spring. Hookes law is named after its creator, British physicist Robert Hooke, who stated in 1678 that the extension is proportional to the force. The law essentially describes a linear relationship between the extension of a spring and the restoring force it gives rise to in the spring; in other words, it takes twice as much force to stretch or compress a spring twice as much. Understanding springs and their direction of force. 2.4K views . How far below the initial position the body descends, and the. 2. k is the spring constant, in Newtons per meter (N/m),. What is Asthma? They inform you that the car will have a mass of 1,000 kilograms, and you have four shock absorbers, each 0.5 meters long, to work with. Start with the equation for the period T = 2pisqrt(m/k)" ", where T - the period of oscillation; m - the mass of the oscillating object; k - a constant of proportionality for a mass on a spring; You need to solve this equation for m, so start by squaring both sides of the equation T^2 = (2pi * sqrt(m/k))^2 T^2 = (2pi)^2 * (sqrt(m/k))^2 T^2 = 4pi^2 * m/k . Round answer to two significant digits. Transport the lab to different planets, slow down time, and observe the velocity and acceleration throughout the oscillation. As long as a spring stays within its elastic limit, you can say that F = kx. What does this mean the spring constant should be? There are two forces acting at the point where the mass is attached to the spring. . Mass on a spring - Where a mass m attached to a spring with spring constant k, will oscillate with a period (T). The minus sign shows that this force is in the opposite direction of the force thats stretching or compressing the spring. wikiHow, Inc. is the copyright holder of this image under U.S. and international copyright laws. Hooke's law deals with springs and their main property - the elasticity. The force resists the displacement and has a direction opposite to it, hence the minus sign. He was a contributing editor at PC Magazine and was on the faculty at both MIT and Cornell. In order to continue enjoying our site, we ask that you confirm your identity as a human. But, if you continue to apply the force beyond the elastic limit, the spring with not return to its original pre-stretched state and will be permanently damaged. A springs elasticity will return to its original form once the outside force, whatever the mass, is removed. The only additional step is translating the mass of the car into a weight (i.e., the force due to gravity acting on the mass) on each wheel. However, after the limit of proportionality for the material in question, the relationship is no longer a straight-line one, and Hookes law ceases to apply. In order to figure out how to calculate the spring constant, we must remember what Hookes law says: Now, we need to rework the equation so that we are calculating for the missing metric, which is the spring constant, or k. Looking only at the magnitudes and therefore omitting the negative sign, you get, The springs used in the shock absorbers must have spring constants of at least 4,900 newtons per meter. What spring constant does the suspension need to have? Assuming these shock absorbers use springs, each one has to support a mass of at least 250 kilograms, which weighs the following:\r\n\r\nF = mg = (250 kg)(9.8 m/s²) = 2,450 N\r\n\r\nwhere F equals force, m equals the mass of the object, and g equals the acceleration due to gravity, 9.8 meters per second². What is the spring constant k for the spring? The value of this constant depends on the qualities of the specific spring, and this can be directly derived from the properties of the spring if needed. You know that the force due to the weight of the car is given by F = mg, where g = 9.81 m/s2, the acceleration due to gravity on Earth, so you can adjust the Hookes law formula as follows: However, only one quarter of the total mass of the car is resting on any wheel, so the mass per spring is 1800 kg / 4 = 450 kg. The force exerted by a spring is called a restoring force; it always acts to restore the spring toward equilibrium. When a spring stays within its elastic limit and obeys Hookes law, the spring is called an ideal spring.